arXiv subjects

Erwan Allys

Publications and source records attributed to Erwan Allys.

31 records · Page 2Linked to original sources

arXiv2022

Wavelet Moments for Cosmological Parameter Estimation

Extracting non-Gaussian information from the non-linear regime of structure formation is key to fully exploiting the rich data from upcoming cosmological surveys probing the large-scale structure of the universe. However, due to theoretical and computational complexities, this remains one of the main challenges in analyzing observational data. We present a set of summary statistics for cosmological matter fields based on 3D wavelets to tackle this challenge. These statistics are computed as the spatial average of the complex modulus of the 3D wavelet transform raised to a power $q$ and are therefore known as invariant wavelet moments. The 3D wavelets are constructed to be radially band-limited and separable on a spherical polar grid and come in three types: isotropic, oriented, and harmonic. In the Fisher forecast framework, we evaluate the performance of these summary statistics on matter fields from the Quijote suite, where they are shown to reach state-of-the-art parameter constraints on the base $Λ$CDM parameters, as well as the sum of neutrino masses. We show that we can improve constraints by a factor 5 to 10 in all parameters with respect to the power spectrum baseline.

astro-ph.CO↗

arXiv2022

Quantification of high dimensional non-Gaussianities and its implication to Fisher analysis in cosmology

It is well known that the power spectrum is not able to fully characterize the statistical properties of non-Gaussian density fields. Recently, many different statistics have been proposed to extract information from non-Gaussian cosmological fields that perform better than the power spectrum. The Fisher matrix formalism is commonly used to quantify the accuracy with which a given statistic can constrain the value of the cosmological parameters. However, these calculations typically rely on the assumption that the likelihood of the considered statistic follows a multivariate Gaussian distribution. In this work we follow Sellentin & Heavens (2017) and use two different statistical tests to identify non-Gaussianities in different statistics such as the power spectrum, bispectrum, marked power spectrum, and wavelet scatering transform (WST). We remove the non-Gaussian components of the different statistics and perform Fisher matrix calculations with the \textit{Gaussianized} statistics using Quijote simulations. We show that constraints on the parameters can change by a factor of $\sim 2$ in some cases. We show with simple examples how statistics that do not follow a multivariate Gaussian distribution can achieve artificially tight bounds on the cosmological parameters when using the Fisher matrix formalism. We think that the non-Gaussian tests used in this work represent a powerful tool to quantify the robustness of Fisher matrix calculations and their underlying assumptions. We release the code used to compute the power spectra, bispectra, and WST that can be run on both CPUs and GPUs.

astro-ph.CO↗

arXiv2021

Single frequency CMB B-mode inference with realistic foregrounds from a single training image

With a single training image and using wavelet phase harmonic augmentation, we present polarized Cosmic Microwave Background (CMB) foreground marginalization in a high-dimensional likelihood-free (Bayesian) framework. We demonstrate robust foreground removal using only a single frequency of simulated data for a BICEP-like sky patch. Using Moment Networks we estimate the pixel-level posterior probability for the underlying {E,B} signal and validate the statistical model with a quantile-type test using the estimated marginal posterior moments. The Moment Networks use a hierarchy of U-Net convolutional neural networks. This work validates such an approach in the most difficult limiting case: pixel-level, noise-free, highly non-Gaussian dust foregrounds with a single training image at a single frequency. For a real CMB experiment, a small number of representative sky patches would provide the training data required for full cosmological inference. These results enable robust likelihood-free, simulation-based parameter and model inference for primordial B-mode detection using observed CMB polarization data.

astro-ph.CO↗

arXiv2021

The Quijote simulations

The Quijote simulations are a set of 44,100 full N-body simulations spanning more than 7,000 cosmological models in the $\{Ω_{\rm m}, Ω_{\rm b}, h, n_s, σ_8, M_ν, w \}$ hyperplane. At a single redshift the simulations contain more than 8.5 trillions of particles over a combined volume of 44,100 $(h^{-1}{\rm Gpc})^3$; each simulation follow the evolution of $256^3$, $512^3$ or $1024^3$ particles in a box of $1~h^{-1}{\rm Gpc}$ length. Billions of dark matter halos and cosmic voids have been identified in the simulations, whose runs required more than 35 million core hours. The Quijote simulations have been designed for two main purposes: 1) to quantify the information content on cosmological observables, and 2) to provide enough data to train machine learning algorithms. In this paper we describe the simulations and show a few of their applications. We also release the Petabyte of data generated, comprising hundreds of thousands of simulation snapshots at multiple redshifts, halo and void catalogs, together with millions of summary statistics such as power spectra, bispectra, correlation functions, marked power spectra, and estimated probability density functions.

astro-ph.CO↗

arXiv2021

A new approach for the statistical denoising of Planck interstellar dust polarization data

Dust emission is the main foreground for cosmic microwave background (CMB) polarization. Its statistical characterization must be derived from the analysis of observational data because the precision required for a reliable component separation is far greater than what is currently achievable with physical models of the turbulent magnetized interstellar medium. This letter takes a significant step toward this goal by proposing a method that retrieves non-Gaussian statistical characteristics of dust emission from noisy Planck polarization observations at 353 GHz. We devised a statistical denoising method based on wavelet phase harmonics (WPH) statistics, which characterize the coherent structures in non-Gaussian random fields and define a generative model of the data. The method was validated on mock data combining a dust map from a magnetohydrodynamic simulation and Planck noise maps. The denoised map reproduces the true power spectrum down to scales where the noise power is an order of magnitude larger than that of the signal. It remains highly correlated to the true emission and retrieves some of its non-Gaussian properties. Applied to Planck data, the method provides a new approach to building a generative model of dust polarization that will characterize the full complexity of the dust emission. We also release PyWPH, a public Python package, to perform GPU-accelerated WPH analyses on images.

astro-ph.CO↗

arXiv2020

Statistical description of dust polarized emission from the diffuse interstellar medium -- A RWST approach

The statistical characterization of the diffuse magnetized ISM and Galactic foregrounds to the CMB poses a major challenge. To account for their non-Gaussian statistics, we need a data analysis approach capable of efficiently quantifying statistical couplings across scales. This information is encoded in the data, but most of it is lost when using conventional tools, such as one-point statistics and power spectra. The wavelet scattering transform (WST), a low-variance statistical descriptor of non-Gaussian processes introduced in data science, opens a path towards this goal. We applied the WST to noise-free maps of dust polarized thermal emission computed from a numerical simulation of MHD turbulence. We analyzed normalized complex Stokes maps and maps of the polarization fraction and polarization angle. The WST yields a few thousand coefficients; some of them measure the amplitude of the signal at a given scale, and the others characterize the couplings between scales and orientations. The dependence on orientation can be fitted with the reduced WST (RWST), an angular model introduced in previous works. The RWST provides a statistical description of the polarization maps, quantifying their multiscale properties in terms of isotropic and anisotropic contributions. It allowed us to exhibit the dependence of the map structure on the orientation of the mean magnetic field and to quantify the non-Gaussianity of the data. We also used RWST coefficients, complemented by additional constraints, to generate random synthetic maps with similar statistics. Their agreement with the original maps demonstrates the comprehensiveness of the statistical description provided by the RWST. This work is a step forward in the analysis of observational data and the modeling of CMB foregrounds. We also release PyWST, a Python package to perform WST/RWST analyses at: https://github.com/bregaldo/pywst.

astro-ph.CO↗

arXiv2017

Beyond standard models in cosmology (In French)

The current description of fundamental interactions is based on two theories with the status of standard models. The electromagnetic and nuclear interactions are described at a quantum level by the Standard Model of particle physics, using tools like gauge theories and spontaneous symmetry breaking by the Higgs mechanism. The gravitational interaction is described on the other hand by general relativity, based on a dynamical description of space-time at a classical level. Although these models are verified to high precision in the solar system experiments, they suffer from several theoretical weaknesses and a lack of predictive power at the Planck scale as well as at cosmological scales; they are thus not viewed anymore as fundamental theories. As its phenomenology involves both these extreme scales, cosmology is then a good laboratory to probe theories going beyond these standard models. The first part of this thesis focus on cosmic strings, topological defects forming during the spontaneous symmetry breaking of grand unified theories in the early universe. I show especially how to study these defects while taking into account the complete structure of the particles physics models leading to their formation, going beyond the standard descriptions in terms of simplified toy-models. The second part is devoted to the construction and the examination of different theories of modified gravity related to the Galileon model, a model which tries in particular to explain the dark energy phenomenology.

astro-ph.CO↗

arXiv2017

New terms for scalar multi-Galileon models and application to SO(N) and SU(N) group representations

We investigate a new class of scalar multi-galileon models, which is not included in the commonly admitted general formulation of generalized multi-galileons. The Lagrangians of this class of models, some of them having already been introduced in previous works, are specific to multi-galileon theories, and vanish in the single galileon case. We examine them in details, discussing in particular some hidden symmetry properties which can be made explicit by adding total derivatives to these Lagrangians. These properties allow us to describe the possible dynamics for these new Lagrangians in the case of multi-galileons in the fundamental representation of a SO(N) and SU(N) global symmetry group, as well as in the adjoint representation of a SU(N) global symmetry group. We perform in parallel an exhaustive examination of some of these models, finding a complete agreement with the dynamics obtained using the symmetry properties. Finally, we conclude by discussing what could be the most general multi-galileon theory, as well as the link between scalar and vector multi-galileon models.

hep-th↗

arXiv2016

Generalized SU(2) Proca Theory

Following previous works on generalized Abelian Proca theory, also called vector Galileon, we investigate the massive extension of an SU(2) gauge theory, i.e., the generalized SU(2) Proca model, which could be dubbed non-Abelian vector Galileon. This particular symmetry group permits fruitful applications in cosmology such as inflation driven by gauge fields. Our approach consists in building, in an exhaustive way, all the Lagrangians containing up to six contracted Lorentz indices. For this purpose, and after identifying by group theoretical considerations all the independent Lagrangians which can be written at these orders, we consider the only linear combinations propagating three degrees of freedom and having healthy dynamics for their longitudinal mode, i.e., whose pure Stückelberg contribution turns into the SU(2) multi-Galileon dynamics. Finally, and after having considered the curved space-time expansion of these Lagrangians, we discuss the form of the theory at all subsequent orders.

hep-th↗

arXiv2016

On the 4D generalized Proca action for an Abelian vector field

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 1405, 015 (2014) and Phys. Lett. B 757, 405 (2016) and complements those of JCAP 1602, 004 (2016). We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field $A_μ$, the Faraday tensor $F_{μν}$ and its Hodge dual $\tilde{F}_{μν}$.

hep-th↗

arXiv2016

Bosonic structure of realistic SO(10) SUSY cosmic strings

We study the bosonic structure of $F$-term Nambu-Goto cosmic strings forming in a realistic SO(10) implementation, assuming standard hybrid inflation. We describe the supersymmetric grand unified theory, and its spontaneous symmetry breaking scheme in parallel with the inflationary process. We also write the explicit tensor formulation of its scalar sector, focusing on the sub-representations singlet under the standard model, which is sufficient to describe the string structure. We then introduce an ansatz for abelian cosmic strings, discussing in details the hypothesis, and write down the field equations and boundary conditions. Finally, after doing a perturbative study of the model, we present and discuss the results obtained with numerical solutions of the string structure.

gr-qc↗

arXiv2016

Bosonic condensates in realistic supersymmetric GUT cosmic strings

We study the realistic structure of F-term Nambu-Goto cosmic strings forming in a general supersymmetric Grand Unified Theory implementation, assuming standard hybrid inflation. Examining the symmetry breaking of the unification gauge group down to the Standard Model, we discuss the minimal field content necessary to describe abelian cosmic strings appearing at the end of inflation. We find that several fields will condense in most theories, questioning the plausible occurrence of associated currents (bosonic and fermionic). We perturbatively evaluate the modification of their energy per unit length due to the condensates. We provide a criterion for comparing the usual abelian Higgs approximation used in cosmology to realistic situations.

gr-qc↗

arXiv2016

Generalized Proca action for an Abelian vector field

We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature.

hep-th↗